Quantum computational calculations of a series of tetrathiafulvalene derivatives linked to N-methylthiocarbamoyl group

We investigate in this study, the quantum chemical computations of a series of tetrathiafulvalene derivatives linked to N-methylthiocarbamoyl group 1-4 using the DFT/B3LYP method with 6-31G (d,p) basis set. The optimized structures and geometrical parameters were determined by the same method cited above. In addition, a molecular electrostatic potential map (MEP) has been analyzed for predicting the reactive sites. The calculated HOMO and LUMO energies showed that charge transfer occurs within the molecule. The chemical reactivity parameters (chemical hardness and softness, electronegativity, chemical potential and electrophilicity index) were discussed clearly. To find out more reactive sites of the title molecules, condensed Fukui functions have been also calculated. Stability of the compounds arising from hyper-conjugative interaction and charge delocalization has been analyzed using Natural bond orbital (NBO) analysis. NLO properties related to polarizability and hyperpolarizability are also discussed to predict the applications of title compounds.


Introduction
Many efforts have been devoted in recent years to the development of new systems containing two or more tetrathiafulvalene (TTF) units [1][2][3].Tetrathiafulvalene (TTF) and its derivatives have been extensively studied due to their versatile behaviors, such as reversible redox properties and strong electron donating capabilities for preparing charge-transfer (CT) salts [4], D-A systems and other fields [5][6][7].Also, they are widely employed as components for both inter-and intramolecular charge transfer materials [8].Owing to their highly conjugated frame-work, they should fulfil some criteria necessary to reveal large third-order nonlinear optical susceptibilities.
Density functional theory (DFT) methods have been used to correlate reactivity with molecular properties including energy, charge, and polarizability [9][10][11].Correlations can be made with the electron density as the central quantity for characterization of molecular properties [12].
In this context we are studying a theoretical investigation of a series of tetrathiafulvalene derivatives linked to Nmethylthiocarbamoyl group 1-4 described in literature [13] by means of Gaussian 09W program within DFT/B3LYP method and 6-31G (d,p) basis set.We carried the optimized geometric parameters, molecular electrostatic potential (MESP) surface and contour map, quantum chemical descriptors (electronegativity, chemical potential, global softness and electrophilicity index) and local density functional descriptors such as Fukui function.The Frontier molecular orbitals (FMOs) analysis was reported to study the molecular reactivity and stability of the molecules.The natural bond orbital (NBO) analysis was also carried out to understand the NLO activity of the title molecules.

Material and methods
The density functional theory DFT/B3LYP with the 6-31 G (d, p) as basis set was adopted to calculate the properties of (TTFs)-N-methylthiocarbamoyl 1-4 in the present work.The entire calculations were performed using Gaussian 09W program package [14].

Molecular geometry
The optimized molecular structures of title molecules obtainedfrom Gauss view is shown in Figure 1.The optimization geometricalparameters of (TTFs)-N-methylthiocarbamoyl 1-4 obtained by B3LYP method with6-31G(d,p) as basis set are listed in Tables 1-4.As seen from the figure 2 that, in all molecules, the regions exhibiting the negative electrostatic potential are localized near TTF core and sulfur atom of N-methylthiocarbamoyl group while the regions presenting the positive potential are localized vicinity of the hydrogen atoms of alkyl and cycled groups.

Frontier molecular orbitals (FMOs)
In principle, there are several ways to calculate the excitation energies.The simplest one involves the difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a neutral system, and is a key parameter determining molecular properties.Both HOMO and LUMO are the main orbital taking part in chemical reaction.The HOMO energy characterizes the ability of electron giving, the LUMO characterizes the ability of electron accepting, and the gap between HOMO and LUMO characterizes the molecular chemical stability [17].The energy gap between the HOMOs and LUMOs is a critical parameter in determining molecular electrical transport properties because it is a measure of electron conductivity [18].Surfaces for the frontier orbitals were drawn to understand the bonding scheme of present compound.It establishes correlation in various chemical and biochemical systems [19][20].There are lot of applications available for the use of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy gap as a quantum chemical descriptor.
The HOMO energies, the LUMO energies and the energy gap for(TTFs)-N-methylthiocarbamoyl1-4have been calculated using B3LYP level with6-31G(d, p) basis set.The pictorial representation of the HOMO and the LUMO for compound 3is shown in Figure 3.

Global reactivity descriptors
The understanding of chemical reactivity and site selectivity of the molecular systems has been effectively handled by the conceptual density functional theory (DFT) [21].Chemical potential, global hardness, global softness, electronegativity and electrophilicity are global reactivity descriptors, highly successful in predicting global chemical reactivity trends.The global parameters descriptors of (TTFs)-N-methylthiocarbamoyl 1-4 such as hardness (η), softness(S), chemical potential (µ), electronegativity (χ) and electrophilicity index (ω) as well as local reactivity descriptors as the Fukui function and the philicity have been defined [22][23][24][25][26].Using Koopman's theorem for closedshell compounds, η, µ, χ can be defined as: Where I and A are the ionization potential and electron affinity of the compounds, respectively.Parr et al. [23] have proposed electrophilicity index (ω) as a measure of energy lowering due to maximal electron flow between donor and acceptor.They defined electrophilicity index (ω) as follows: The electrophilicity is a descriptor of reactivity that allows a quantitative classification of the global electrophilic nature of a molecule within a relative scale.All the calculated values of HOMO-LUMO, energy gap, ionization potential, electron affinity, hardness, potential, softness and electrophilicity index are obtained by B3LYP/6-31G( d, p) method and shown in Table 5.As presented in table 5, the compound which have the lowest energetic gap is the compound 3 (∆Egap = 2.363 eV).This lower gap allows it to be the softest molecule.The compound that have the highest energy gap is the compound 1 (∆Egap = 9.226 eV).The compound that has the highest HOMO energy is the compound 3 (EHOMO = -4.383eV).This higher energy allows it to be the best electron donor.The compound that has the lowest LUMO energy is the compound 3 (ELUMO = -2.020eV) which signifies that it can be the best electron acceptor.The two properties like I (potential ionization) and A (affinity) are so important, the determination of these two properties allow us to calculate the absolute electronegativity (χ) and the absolute hardness (η).These two parameters are related to the one-electron orbital energies of the HOMO and LUMO respectively.Compound 3 has lowest value of the potential ionization (I = 4.383 eV), so that will be the better electron donor.Compound 3 has the largest value of the affinity (A = 2.020 eV), so it is the better electron acceptor.The chemical reactivity varies with the structural of molecules.Chemical hardness (softness) value of compound 3 (η = 1.181 eV, S = 0.423 eV) is lesser (greater) among all the molecules.Thus, compound 4 is found to be more reactive than all the compounds.Compound 4 possesses higher electronegativity value (χ = 3.872 eV) than all compounds so; it is the best electron acceptor.The value of ω for compound 3 (ω = 4.339 eV) indicates that it is the stronger electrophiles than all compounds.Compound 3 has the smaller frontier orbital gap so, it is more polarizable and is associated with a high chemical reactivity, low kinetic stability and is also termed as soft molecule.

Local reactivity descriptors
The local reactivity has been analyzed by means of Fukui indices [27], an indication of the reactive centers within the molecules.These are measurement of the chemical reactivity, as well as an indicative of the reactive regions, nucleophilic and electrophilic behavior of the molecule [28].The local (condensed) Fukui functions (f + k; f -k; f 0 k) are calculated using the procedure proposed by Yang and Mortier [29] based on a finite difference method are calculated at same calculation method B3LYP/6-31G (d,p) using for nucleophilic attack for electrophilic attack for radical attack Where q (N), q (N+1), and q (N-1) are the electronic population of the atom k in neutral, cationic and anionic systems respectively [30].The reactive sites on (TTFs)-N-methylthiocarbamoyl 1-4 are calculated by the DFT/B3LYP method with 6-31G (d,p) basis set and shown in Tables 6-7.-0.007 -0.011 -0.011 -0.012 f 0 -0.015 -0.016 -0.018 -0.024 f + : Fukui functions for nucleophilic attack, f -: Fukui functions for electrophilic attack, f 0 : Fukui functions for radical attack.
From the tables 6-7, the parameters of local reactivity descriptors show that 4C and 13N are the more reactive sites in compounds 1, 2, 3 and 4 respectively for nucleophilic attacks.The more reactive sites in radical attacks are 4C, 2C, forcompounds 1, 4 respectively and 12C for the both compounds 2 and 3.The more reactive sites for electrophilic attacks are 11C for compound 1 and 12C for compounds 2, 3 and 4 respectively.

Natural bond orbital analysis (NBO)
Natural bond orbitals offers a handy basis for exploring charge transfer or conjugative interaction in molecular systems and is an efficient method for studying intra-and inter molecular bonding and interaction among bonds.In order to investigate the intra and intermolecular interactions, the stabilization energies of (TTFs)-Nmethylthiocarbamoyl 1-4were performed by using second-order perturbation theory.For each donor NBO(i) and acceptor NBO(j), the stabilization energy E2 associated with electron delocalization between donor and acceptor is estimated as [31,32].

Nonlinear optical properties (NLO)
The NLO activity provide the key functions for frequency shifting, optical modulation, optical switching and optical logic for the developing technologies in areas such as communication, signal processing and optical interconnections [34].In the presence of an applied electric field, the energy of a system is a function of the electric field and the first hyperpolarizability is a third rank tensor that can be described by a 3×3×3matrix.The 27 components of the 3D matrix can be reduced to10 components because of the Kleinman symmetry [35].The matrix can be given in the lower tetrahedral format.It is obvious that the lower part of the 3×3×3 matrices is a tetrahedral.The components of first hyperpolarizability (β) are defined as the coefficients in the Taylor series expansion of the energy in the external electric field.When the external electric field is weak and homogeneous, this expansion is given below: ...
Where E 0 is the energy of the unperturbed molecules, Fα is the field at the origin, µα, ααβ and βαβγ are the components of dipole moment, polarizability and first hyperpolarizability, respectively.The total static dipole moments µ, the mean polarizabilities α0, the anisotropy of the polarizabilities Δα and the mean first hyperpolarizabilities β, using the x, y and z components they are defined as [36,37]: The polarizability (α0) and the hyper polarizability (β),the anisotropy of the polarizability (Δα)and the electric dipole moment (µ) of(TTFs)-N-methylthiocarbamoyl 1-4 are calculated by finite field method using B3LYP/6-31G (d,p) basis set and listed in Table 12.
Since the values of the polarizabilities (∆α) and the hyperpolarizabilities (β) of the GAUSSIAN 09 output are obtained in atomic units (a.u.), the calculated values have been converted into electrostatic units (e.s.u.) (for α; 1 a.u = 0.1482 x 10 -24 e.s.u., for β; 1 a.u = 8.6393 x 10 -33 e.s.u.).The calculated values of dipole moment (µ) for the title compounds were found to be 5.5574, 4.6495, 3.8982 and 3.9329 D respectively, which are approximately two times than to the value for urea (µ = 1.3732D).Urea is one of the prototypical moleculesused in the study of the NLO properties of molecular systems.Therefore, it has been used frequently as a threshold value for comparative purposes.The calculated values of polarizability are 56.8207x 10 -24 , 60.9411 x 10 -24 , 75.0280 x 10 -24 and 81.2628 x 10 -24 esu respectively; the values of anisotropy of the polarizability are 8.4208, 9.0315, 11.1191 and 12.0431 esu, respectively.The magnitude of the molecular hyperpolarizability (β) is one of important key factors in a NLO system.The DFT/6-31G (d,p) calculated first hyperpolarizability value (β) of (TTFs)-N-methylthiocarbamoyl molecules are equal to 120.8723 x 10 -33 , 86.6131 x 10 -33 , 269.4594 x 10 -33 and 109.2424x 10 -33 esu.The first hyperpolarizability of title molecules is approximately 0.35, 0.25, 0.78 and 0.32 times than those of urea (β of urea is 343.272x10 -33 esu obtained by B3LYP/6-311G (d,p) method).The above results show that (TTFs)-N-methylthiocarbamoyl 1-4 might have not the NLO applications.

Conclusion
With this research, we have successfully contributed to quantum computational calculations study of a (TTFs)-Nmethylthiocarbamoyl.The results of quantum chemical descriptors show that compound 3 has the smaller frontier orbital gap so, it is more polarizable and is associated with a high chemical reactivity, low kinetic stability and is also termed as soft molecule.The MEP map contour shows that the regions exhibiting the negative electrostatic potential are localized near TTF core and sulfur atom of N-methylthiocarbamoyl group while the regions presenting the positive potential are localized vicinity of the hydrogen atoms of alkyl and cycled groups.NBO analysis reveals that the important intramolecular charge transfer causing stabilization of the system to the title molecule and the intramolecular conjugative interaction lead to highest stabilization.NLO results show that (TTFs)-Nmethylthiocarbamoyl have not nonlinear optical applications.

3. 2 .Figure 2
Figure 2 Molecular electrostatic potential surface of (TTFs)-N-methylthiocarbamoyl 1-4 An electron density iso-surface mapped with electrostatic potential surface depicts the size, shape, charge density and site of chemical reactivity of the molecules.MEP shown in figure 2 calculated by DFT/B3LYP method with 6-31G (d, p)

Figure 3
Figure 3 HOMO-LUMO Structure with the energy level diagram of compound 3

Table 1
Optimized geometric parameters of compound 1

Table 2
Optimized geometric parameters of compound 2

Table 6
Order of the reactive sites on compounds 1 and 2 + : Fukui functions for nucleophilic attack, f -: Fukui functions for electrophilic attack, f 0 : Fukui functions for radical attack. f

Table 7
Order of the reactive sites on compounds 3 and 4

Table 8
Second order perturbation theory analysis of Fock matrix on NBO of compound 1

Table 9
Second order perturbation theory analysis of Fock matrix on NBO of compound 2

Table 10
Second order perturbation theory analysis of Fock matrix on NBO of compound 3

Table 11
Second order perturbation theory analysis of Fock matrix on NBO of compound 4